It looks okay, but I am trying to find out how to center it instead of it being left aligned.
Add this on the Custom CSS option.
#header-logo {
display: table;
float: none;
margin: 0 auto;
}I intend to fill the entire header with the logo.
A Header Background (Dashboard -> Appearance -> Header) is more suited for this job than a Header Logo. But if you really want to use the logo to fill the area then you can look for the ideal size also on the Header Background page.